Central plant with automatic subplant models

ABSTRACT

A method includes finding, in subplant performance data points defined by values of an independent variable and values of a dependent variable, a first point for which a convexity metric of the dependent variable with respect to the independent variable exceeds a threshold, creating a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point, and controlling the campus subplant based on the subplant curve.

BACKGROUND

The present disclosure relates generally to a central plant or central energy facility configured to serve the energy loads of a building or campus. The present disclosure relates more particular to a central plant with an asset allocator configured to determine an optimal distribution of the energy loads across various subplants of the central plant.

A central plant typically includes multiple subplants configured to serve different types of energy loads. For example, a central plant may include a chiller subplant configured to serve cooling loads, a heater subplant configured to serve heating loads, and/or an electricity subplant configured to serve electric loads. A central plant purchases resources from utilities to run the subplants to meet the loads.

Some central plants include energy storage. Energy storage may be a tank of water that stores hot water for campus heating, an ice tank for campus cooling, and/or battery storage. In the presence of real-time pricing from utilities, it may be advantageous to manipulate the time that a certain resource or energy type is consumed. Instead of producing the resource exactly when it is required by the load, it can be optimal to produce that resource at a time when the production cost is low, store it, and then use it when the resource needed to produce that type of energy is more expensive. It can be difficult and challenging to optimally allocate the energy loads across the assets of the central plant.

SUMMARY

One implementation of the present disclosure is a method of operating a campus subplant. The method includes finding, in subplant performance data points defined by values of an independent variable and values of a dependent variable, a first point for which a convexity metric of the dependent variable with respect to the independent variable exceeds a threshold, creating a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point, and controlling the campus subplant based on the subplant curve.

In some embodiments, the method also includes finding, in the subplant performance data points, a second point for which the convexity metric exceeds the threshold. Creating the subplant curve can include providing the first convex region between the first point and the second point and providing a third convex region such that the second point is between the first convex region and the third convex region. In some embodiments, the convexity metric is a second derivative, the threshold is zero, and the convexity metric exceeds the threshold when the second derivative is less than zero. The method may include calculating the second derivatives for the subplant performance data points and ranking a subset of the subplant performance data points from most negative second derivative to least negative second derivative, where the first point has the most negative second derivative and the second point has a next most negative second derivative.

In some embodiments, the method includes, in response to the subplant curve satisfying a criterion, providing the subplant curve for use in controlling the campus subplant and, in response to the subplant curve not satisfying the criterion, splitting the first convex region or the second convex region at a second point for which the convexity metric exceeds the threshold. In some embodiments, the criterion is at least one of a maximum number of convex regions, an accuracy threshold, or that the convexity metric does not exceed the threshold for a remainder of the subplant performance data points.

In some embodiments, controlling the campus subplant based on the subplant curve includes performing an optimization subject to a constraint based on the subplant curve to determine control decisions for the campus subplant. In some embodiments, the independent variable represents production by the campus subplant and the dependent variable represents consumption by the campus subplant.

Another implementation of the present disclosure is non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause the one or more processors to perform operations. The operations include finding, in subplant performance data points defined by values of an independent variable and values of a dependent variable, a first point for which a convexity metric of the dependent variable with respect to the independent variable exceeds a threshold, creating a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point, and controlling a campus subplant based on the subplant curve.

In some embodiments, the operations also include finding, in the subplant performance data points, a second point for which the convexity metric exceeds the threshold. Creating the subplant curve can include providing the first convex region between the first point and the second point and providing a third convex region such that the second point is between the first convex region and the third convex region. The operations can include calculating the convexity metrics for the subplant performance data points and ranking a subset of the subplant performance data points by amounts by which the convexity metrics exceed the threshold. In this example the first point has the convexity metric which exceeds the threshold by a greatest amount and the second point has the convexity metric which exceeds the threshold by a next greatest amount.

In some embodiments, the convexity metric is a second derivative, the threshold is zero, and the convexity metric exceeds the threshold when the second derivative is less than zero.

In some embodiments, the operations also include providing the subplant curve for use in controlling the campus subplant in response to subplant curve satisfying a criterion; and splitting the first convex region or the second convex region at a second point for which the convexity metric exceeds the threshold in response to the subplant curve not satisfying the criterion. In some embodiments, the criterion is satisfied if a maximum number of convex regions is reached, an accuracy threshold is reached, or the convexity metric does not exceed the threshold for a remainder of the subplant performance data points.

controlling the campus subplant based on the subplant curve comprises performing an optimization subject to a constraint based on the subplant curve to determine control decisions for the campus subplant. In some embodiments, the independent variable represents production by the campus subplant and the dependent variable represents consumption by the campus subplant.

Another implementation of the present disclosure is a central plant. The central plant includes a subplant operable to consume a first resource and produce a second resource according to a set of subplant performance data points relating consumption amounts to production amounts. The central plant includes circuitry programmed to find a first point in the subplant performance data points for which a convexity metric of the consumption amounts with respect to the production amounts exceeds a threshold, create a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point, and control the subplant to consume the first resource and produce the second resource by executing control logic that uses the subplant curve.

In some embodiments, the circuitry is also programmed to compare the subplant curve to a criterion, use the subplant curve in the control logic in response to the subplant curve satisfying the criterion, and split the first convex region or the second convex region at an additional point for which the convexity metric exceeds the threshold before using the subplant curve in the control logic in response to the subplant curve not satisfying the criterion. In some embodiments, the criterion is a maximum number of convex regions or an accuracy threshold. In some embodiments, the convexity metric is a second derivative, the threshold is zero, and the convexity metric exceeds the threshold when the second derivative is less than zero.

BRIEF DESCRIPTION OF THE DRAWINGS

Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements.

FIG. 1 is a drawing of a building equipped with a HVAC system, according to an exemplary embodiment.

FIG. 2 is a block diagram of a central plant which can be used to serve the energy loads of the building of FIG. 1 , according to an exemplary embodiment.

FIG. 3 is a block diagram of an airside system which can be implemented in the building of FIG. 1 , according to an exemplary embodiment.

FIG. 4 is a block diagram of an asset allocation system including sources, subplants, storage, sinks, and an asset allocator configured to optimize the allocation of these assets, according to according to some embodiments.

FIG. 5 is a block diagram of a central plant controller in which the asset allocator of FIG. 4 can be implemented, according to some embodiments.

FIG. 6 is a flowchart of a process for generating a subplant curve for use by the asset allocating in optimizing asset allocations, according to some embodiments.

FIG. 7 is a set of graphs illustrating features relating to the process of FIG. 6 , according to some embodiments.

FIG. 8 is another set of graphs illustrating features relating to the process of FIG. 6 , according to some embodiments.

FIG. 9 is a graphical visualization of error calculations used in some embodiments of FIG. 6 , according to some embodiments.

DETAILED DESCRIPTION Overview

Referring generally to the FIGURES, a central plant with an asset allocator and components thereof are shown, according to various exemplary embodiments. The asset allocator can be configured to manage energy assets such as central plant equipment, battery storage, and other types of equipment configured to serve the energy loads of a building. The asset allocator can determine an optimal distribution of heating, cooling, electricity, and energy loads across different subplants (i.e., equipment groups) of the central plant capable of producing that type of energy.

In some embodiments, the asset allocator is configured to control the distribution, production, storage, and usage of resources in the central plant. The asset allocator can be configured to minimize the economic cost (or maximize the economic value) of operating the central plant over a duration of an optimization period. The economic cost may be defined by a cost function J(x) that expresses economic cost as a function of the control decisions made by the asset allocator. The cost function J(x) may account for the cost of resources purchased from various sources, as well as the revenue generated by selling resources (e.g., to an energy grid) or participating in incentive programs.

The asset allocator can be configured to define various sources, subplants, storage, and sinks. These four categories of objects define the assets of a central plant and their interaction with the outside world. Sources may include commodity markets or other suppliers from which resources such as electricity, water, natural gas, and other resources can be purchased or obtained. Sinks may include the requested loads of a building or campus as well as other types of resource consumers. Subplants are the main assets of a central plant. Subplants can be configured to convert resource types, making it possible to balance requested loads from a building or campus using resources purchased from the sources. Storage can be configured to store energy or other types of resources for later use.

In some embodiments, the asset allocator performs an optimization process to determine an optimal set of control decisions for each time step within the optimization period. The control decisions may include, for example, an optimal amount of each resource to purchase from the sources, an optimal amount of each resource to produce or convert using the subplants, an optimal amount of each resource to store or remove from storage, an optimal amount of each resource to sell to resources purchasers, and/or an optimal amount of each resource to provide to other sinks. In some embodiments, the asset allocator is configured to optimally dispatch all campus energy assets (i.e., the central plant equipment) in order to meet the requested heating, cooling, and electrical loads of the campus for each time step within the optimization period. These and other features of the asset allocator are described in greater detail below.

Building and HVAC System

Referring now to FIG. 1 , a perspective view of a building 10 is shown. Building 10 can be served by a building management system (BMS). A BMS is, in general, a system of devices configured to control, monitor, and manage equipment in or around a building or building area. A BMS can include, for example, a HVAC system, a security system, a lighting system, a fire alerting system, any other system that is capable of managing building functions or devices, or any combination thereof.

The BMS that serves building 10 may include a HVAC system 100. HVAC system 100 can include a plurality of HVAC devices (e.g., heaters, chillers, air handling units, pumps, fans, thermal energy storage, etc.) configured to provide heating, cooling, ventilation, or other services for building 10. For example, HVAC system 100 is shown to include a waterside system 120 and an airside system 130. Waterside system 120 may provide a heated or chilled fluid to an air handling unit of airside system 130. Airside system 130 may use the heated or chilled fluid to heat or cool an airflow provided to building 10. In some embodiments, waterside system 120 can be replaced with or supplemented by a central plant or central energy facility (described in greater detail with reference to FIG. 2 ). An example of an airside system which can be used in HVAC system 100 is described in greater detail with reference to FIG. 3 .

HVAC system 100 is shown to include a chiller 102, a boiler 104, and a rooftop air handling unit (AHU) 106. Waterside system 120 may use boiler 104 and chiller 102 to heat or cool a working fluid (e.g., water, glycol, etc.) and may circulate the working fluid to AHU 106. In various embodiments, the HVAC devices of waterside system 120 can be located in or around building 10 (as shown in FIG. 1 ) or at an offsite location such as a central plant (e.g., a chiller plant, a steam plant, a heat plant, etc.). The working fluid can be heated in boiler 104 or cooled in chiller 102, depending on whether heating or cooling is required in building 10. Boiler 104 may add heat to the circulated fluid, for example, by burning a combustible material (e.g., natural gas) or using an electric heating element. Chiller 102 may place the circulated fluid in a heat exchange relationship with another fluid (e.g., a refrigerant) in a heat exchanger (e.g., an evaporator) to absorb heat from the circulated fluid. The working fluid from chiller 102 and/or boiler 104 can be transported to AHU 106 via piping 108.

AHU 106 may place the working fluid in a heat exchange relationship with an airflow passing through AHU 106 (e.g., via one or more stages of cooling coils and/or heating coils). The airflow can be, for example, outside air, return air from within building 10, or a combination of both. AHU 106 may transfer heat between the airflow and the working fluid to provide heating or cooling for the airflow. For example, AHU 106 can include one or more fans or blowers configured to pass the airflow over or through a heat exchanger containing the working fluid. The working fluid may then return to chiller 102 or boiler 104 via piping 110.

Airside system 130 may deliver the airflow supplied by AHU 106 (i.e., the supply airflow) to building 10 via air supply ducts 112 and may provide return air from building 10 to AHU 106 via air return ducts 114. In some embodiments, airside system 130 includes multiple variable air volume (VAV) units 116. For example, airside system 130 is shown to include a separate VAV unit 116 on each floor or zone of building 10. VAV units 116 can include dampers or other flow control elements that can be operated to control an amount of the supply airflow provided to individual zones of building 10. In other embodiments, airside system 130 delivers the supply airflow into one or more zones of building 10 (e.g., via supply ducts 112) without using intermediate VAV units 116 or other flow control elements. AHU 106 can include various sensors (e.g., temperature sensors, pressure sensors, etc.) configured to measure attributes of the supply airflow. AHU 106 may receive input from sensors located within AHU 106 and/or within the building zone and may adjust the flow rate, temperature, or other attributes of the supply airflow through AHU 106 to achieve setpoint conditions for the building zone.

Central Plant

Referring now to FIG. 2 , a block diagram of a central plant 200 is shown, according to some embodiments. In various embodiments, central plant 200 can supplement or replace waterside system 120 in HVAC system 100 or can be implemented separate from HVAC system 100. When implemented in HVAC system 100, central plant 200 can include a subset of the HVAC devices in HVAC system 100 (e.g., boiler 104, chiller 102, pumps, valves, etc.) and may operate to supply a heated or chilled fluid to AHU 106. The HVAC devices of central plant 200 can be located within building 10 (e.g., as components of waterside system 120) or at an offsite location such as a central energy facility that serves multiple buildings.

Central plant 200 is shown to include a plurality of subplants 202-208. Subplants 202-208 can be configured to convert energy or resource types (e.g., water, natural gas, electricity, etc.). For example, subplants 202-208 are shown to include a heater subplant 202, a heat recovery chiller subplant 204, a chiller subplant 206, and a cooling tower subplant 208. In some embodiments, subplants 202-208 consume resources purchased from utilities to serve the energy loads (e.g., hot water, cold water, electricity, etc.) of a building or campus. For example, heater subplant 202 can be configured to heat water in a hot water loop 214 that circulates the hot water between heater subplant 202 and building 10. Similarly, chiller subplant 206 can be configured to chill water in a cold water loop 216 that circulates the cold water between chiller subplant 206 building 10.

Heat recovery chiller subplant 204 can be configured to transfer heat from cold water loop 216 to hot water loop 214 to provide additional heating for the hot water and additional cooling for the cold water. Condenser water loop 218 may absorb heat from the cold water in chiller subplant 206 and reject the absorbed heat in cooling tower subplant 208 or transfer the absorbed heat to hot water loop 214. In various embodiments, central plant 200 can include an electricity subplant (e.g., one or more electric generators) configured to generate electricity or any other type of subplant configured to convert energy or resource types.

Hot water loop 214 and cold water loop 216 may deliver the heated and/or chilled water to air handlers located on the rooftop of building 10 (e.g., AHU 106) or to individual floors or zones of building 10 (e.g., VAV units 116). The air handlers push air past heat exchangers (e.g., heating coils or cooling coils) through which the water flows to provide heating or cooling for the air. The heated or cooled air can be delivered to individual zones of building 10 to serve thermal energy loads of building 10. The water then returns to subplants 202-208 to receive further heating or cooling.

Although subplants 202-208 are shown and described as heating and cooling water for circulation to a building, it is understood that any other type of working fluid (e.g., glycol, CO₂, etc.) can be used in place of or in addition to water to serve thermal energy loads. In other embodiments, subplants 202-208 may provide heating and/or cooling directly to the building or campus without requiring an intermediate heat transfer fluid. These and other variations to central plant 200 are within the teachings of the present disclosure.

Each of subplants 202-208 can include a variety of equipment configured to facilitate the functions of the subplant. For example, heater subplant 202 is shown to include a plurality of heating elements 220 (e.g., boilers, electric heaters, etc.) configured to add heat to the hot water in hot water loop 214. Heater subplant 202 is also shown to include several pumps 222 and 224 configured to circulate the hot water in hot water loop 214 and to control the flow rate of the hot water through individual heating elements 220. Chiller subplant 206 is shown to include a plurality of chillers 232 configured to remove heat from the cold water in cold water loop 216. Chiller subplant 206 is also shown to include several pumps 234 and 236 configured to circulate the cold water in cold water loop 216 and to control the flow rate of the cold water through individual chillers 232.

Heat recovery chiller subplant 204 is shown to include a plurality of heat recovery heat exchangers 226 (e.g., refrigeration circuits) configured to transfer heat from cold water loop 216 to hot water loop 214. Heat recovery chiller subplant 204 is also shown to include several pumps 228 and 230 configured to circulate the hot water and/or cold water through heat recovery heat exchangers 226 and to control the flow rate of the water through individual heat recovery heat exchangers 226. Cooling tower subplant 208 is shown to include a plurality of cooling towers 238 configured to remove heat from the condenser water in condenser water loop 218. Cooling tower subplant 208 is also shown to include several pumps 240 configured to circulate the condenser water in condenser water loop 218 and to control the flow rate of the condenser water through individual cooling towers 238.

In some embodiments, one or more of the pumps in central plant 200 (e.g., pumps 222, 224, 228, 230, 234, 236, and/or 240) or pipelines in central plant 200 include an isolation valve associated therewith. Isolation valves can be integrated with the pumps or positioned upstream or downstream of the pumps to control the fluid flows in central plant 200. In various embodiments, central plant 200 can include more, fewer, or different types of devices and/or subplants based on the particular configuration of central plant 200 and the types of loads served by central plant 200.

Still referring to FIG. 2 , central plant 200 is shown to include hot thermal energy storage (TES) 210 and cold thermal energy storage (TES) 212. Hot TES 210 and cold TES 212 can be configured to store hot and cold thermal energy for subsequent use. For example, hot TES 210 can include one or more hot water storage tanks 242 configured to store the hot water generated by heater subplant 202 or heat recovery chiller subplant 204. Hot TES 210 may also include one or more pumps or valves configured to control the flow rate of the hot water into or out of hot TES tank 242.

Similarly, cold TES 212 can include one or more cold water storage tanks 244 configured to store the cold water generated by chiller subplant 206 or heat recovery chiller subplant 204. Cold TES 212 may also include one or more pumps or valves configured to control the flow rate of the cold water into or out of cold TES tanks 244. In some embodiments, central plant 200 includes electrical energy storage (e.g., one or more batteries) or any other type of device configured to store resources. The stored resources can be purchased from utilities, generated by central plant 200, or otherwise obtained from any source.

Airside System

Referring now to FIG. 3 , a block diagram of an airside system 300 is shown, according to some embodiments. In various embodiments, airside system 300 may supplement or replace airside system 130 in HVAC system 100 or can be implemented separate from HVAC system 100. When implemented in HVAC system 100, airside system 300 can include a subset of the HVAC devices in HVAC system 100 (e.g., AHU 106, VAV units 116, ducts 112-114, fans, dampers, etc.) and can be located in or around building 10. Airside system 300 may operate to heat or cool an airflow provided to building 10 using a heated or chilled fluid provided by central plant 200.

Airside system 300 is shown to include an economizer-type air handling unit (AHU) 302. Economizer-type AHUs vary the amount of outside air and return air used by the air handling unit for heating or cooling. For example, AHU 302 may receive return air 304 from building zone 306 via return air duct 308 and may deliver supply air 310 to building zone 306 via supply air duct 312. In some embodiments, AHU 302 is a rooftop unit located on the roof of building 10 (e.g., AHU 106 as shown in FIG. 1 ) or otherwise positioned to receive both return air 304 and outside air 314. AHU 302 can be configured to operate exhaust air damper 316, mixing damper 318, and outside air damper 320 to control an amount of outside air 314 and return air 304 that combine to form supply air 310. Any return air 304 that does not pass through mixing damper 318 can be exhausted from AHU 302 through exhaust damper 316 as exhaust air 322.

Each of dampers 316-320 can be operated by an actuator. For example, exhaust air damper 316 can be operated by actuator 324, mixing damper 318 can be operated by actuator 326, and outside air damper 320 can be operated by actuator 328. Actuators 324-328 may communicate with an AHU controller 330 via a communications link 332. Actuators 324-328 may receive control signals from AHU controller 330 and may provide feedback signals to AHU controller 330. Feedback signals can include, for example, an indication of a current actuator or damper position, an amount of torque or force exerted by the actuator, diagnostic information (e.g., results of diagnostic tests performed by actuators 324-328), status information, commissioning information, configuration settings, calibration data, and/or other types of information or data that can be collected, stored, or used by actuators 324-328. AHU controller 330 can be an economizer controller configured to use one or more control algorithms (e.g., state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, feedback control algorithms, etc.) to control actuators 324-328.

Still referring to FIG. 3 , AHU 302 is shown to include a cooling coil 334, a heating coil 336, and a fan 338 positioned within supply air duct 312. Fan 338 can be configured to force supply air 310 through cooling coil 334 and/or heating coil 336 and provide supply air 310 to building zone 306. AHU controller 330 may communicate with fan 338 via communications link 340 to control a flow rate of supply air 310. In some embodiments, AHU controller 330 controls an amount of heating or cooling applied to supply air 310 by modulating a speed of fan 338.

Cooling coil 334 may receive a chilled fluid from central plant 200 (e.g., from cold water loop 216) via piping 342 and may return the chilled fluid to central plant 200 via piping 344. Valve 346 can be positioned along piping 342 or piping 344 to control a flow rate of the chilled fluid through cooling coil 334. In some embodiments, cooling coil 334 includes multiple stages of cooling coils that can be independently activated and deactivated (e.g., by AHU controller 330, by BMS controller 366, etc.) to modulate an amount of cooling applied to supply air 310.

Heating coil 336 may receive a heated fluid from central plant 200 (e.g., from hot water loop 214) via piping 348 and may return the heated fluid to central plant 200 via piping 350. Valve 352 can be positioned along piping 348 or piping 350 to control a flow rate of the heated fluid through heating coil 336. In some embodiments, heating coil 336 includes multiple stages of heating coils that can be independently activated and deactivated (e.g., by AHU controller 330, by BMS controller 366, etc.) to modulate an amount of heating applied to supply air 310.

Each of valves 346 and 352 can be controlled by an actuator. For example, valve 346 can be controlled by actuator 354 and valve 352 can be controlled by actuator 356. Actuators 354-356 may communicate with AHU controller 330 via communications links 358-360. Actuators 354-356 may receive control signals from AHU controller 330 and may provide feedback signals to controller 330. In some embodiments, AHU controller 330 receives a measurement of the supply air temperature from a temperature sensor 362 positioned in supply air duct 312 (e.g., downstream of cooling coil 334 and/or heating coil 336). AHU controller 330 may also receive a measurement of the temperature of building zone 306 from a temperature sensor 364 located in building zone 306.

In some embodiments, AHU controller 330 operates valves 346 and 352 via actuators 354-356 to modulate an amount of heating or cooling provided to supply air 310 (e.g., to achieve a setpoint temperature for supply air 310 or to maintain the temperature of supply air 310 within a setpoint temperature range). The positions of valves 346 and 352 affect the amount of heating or cooling provided to supply air 310 by cooling coil 334 or heating coil 336 and may correlate with the amount of energy consumed to achieve a desired supply air temperature. AHU 330 may control the temperature of supply air 310 and/or building zone 306 by activating or deactivating coils 334-336, adjusting a speed of fan 338, or a combination of both.

Still referring to FIG. 3 , airside system 300 is shown to include a building management system (BMS) controller 366 and a client device 368. BMS controller 366 can include one or more computer systems (e.g., servers, supervisory controllers, subsystem controllers, etc.) that serve as system level controllers, application or data servers, head nodes, or master controllers for airside system 300, central plant 200, HVAC system 100, and/or other controllable systems that serve building 10. BMS controller 366 may communicate with multiple downstream building systems or subsystems (e.g., HVAC system 100, a security system, a lighting system, central plant 200, etc.) via a communications link 370 according to like or disparate protocols (e.g., LON, BACnet, etc.). In various embodiments, AHU controller 330 and BMS controller 366 can be separate (as shown in FIG. 3 ) or integrated. In an integrated implementation, AHU controller 330 can be a software module configured for execution by a processor of BMS controller 366.

In some embodiments, AHU controller 330 receives information from BMS controller 366 (e.g., commands, setpoints, operating boundaries, etc.) and provides information to BMS controller 366 (e.g., temperature measurements, valve or actuator positions, operating statuses, diagnostics, etc.). For example, AHU controller 330 may provide BMS controller 366 with temperature measurements from temperature sensors 362-364, equipment on/off states, equipment operating capacities, and/or any other information that can be used by BMS controller 366 to monitor or control a variable state or condition within building zone 306.

Client device 368 can include one or more human-machine interfaces or client interfaces (e.g., graphical user interfaces, reporting interfaces, text-based computer interfaces, client-facing web services, web servers that provide pages to web clients, etc.) for controlling, viewing, or otherwise interacting with HVAC system 100, its subsystems, and/or devices. Client device 368 can be a computer workstation, a client terminal, a remote or local interface, or any other type of user interface device. Client device 368 can be a stationary terminal or a mobile device. For example, client device 368 can be a desktop computer, a computer server with a user interface, a laptop computer, a tablet, a smartphone, a PDA, or any other type of mobile or non-mobile device. Client device 368 may communicate with BMS controller 366 and/or AHU controller 330 via communications link 372.

Asset Allocation System

Referring now to FIG. 4 , a block diagram of an asset allocation system 400 is shown, according to an exemplary embodiment. Asset allocation system 400 can be configured to manage energy assets such as central plant equipment, battery storage, and other types of equipment configured to serve the energy loads of a building. Asset allocation system 400 can determine an optimal distribution of heating, cooling, electricity, and energy loads across different subplants (i.e., equipment groups) capable of producing that type of energy. In some embodiments, asset allocation system 400 is implemented as a component of central plant 200 and interacts with the equipment of central plant 200 in an online operational environment (e.g., performing real-time control of the central plant equipment). In other embodiments, asset allocation system 400 can be implemented as a component of a planning tool (described with reference to FIGS. 7-8 ) and can be configured to simulate the operation of a central plant over a predetermined time period for planning, budgeting, and/or design considerations.

Asset allocation system 400 is shown to include sources 410, subplants 420, storage 430, and sinks 440. These four categories of objects define the assets of a central plant and their interaction with the outside world. Sources 410 may include commodity markets or other suppliers from which resources such as electricity, water, natural gas, and other resources can be purchased or obtained. Sources 410 may provide resources that can be used by asset allocation system 400 to satisfy the demand of a building or campus. For example, sources 410 are shown to include an electric utility 411, a water utility 412, a natural gas utility 413, a photovoltaic (PV) field (e.g., a collection of solar panels), an energy market 415, and source M 416, where M is the total number of sources 410. Resources purchased from sources 410 can be used by subplants 420 to produce generated resources (e.g., hot water, cold water, electricity, steam, etc.), stored in storage 430 for later use, or provided directly to sinks 440.

Subplants 420 are shown to include a heater subplant 421, a chiller subplant 422, a heat recovery chiller subplant 423, a steam subplant 424, an electricity subplant 425, and subplant N, where N is the total number of subplants 420. In some embodiments, subplants 420 include some or all of the subplants of central plant 200, as described with reference to FIG. 2 . For example, subplants 420 can include heater subplant 202, heat recovery chiller subplant 204, chiller subplant 206, and/or cooling tower subplant 208.

Subplants 420 can be configured to convert resource types, making it possible to balance requested loads from the building or campus using resources purchased from sources 410. For example, heater subplant 421 may be configured to generate hot thermal energy (e.g., hot water) by heating water using electricity or natural gas. Chiller subplant 422 may be configured to generate cold thermal energy (e.g., cold water) by chilling water using electricity. Heat recovery chiller subplant 423 may be configured to generate hot thermal energy and cold thermal energy by removing heat from one water supply and adding the heat to another water supply. Steam subplant 424 may be configured to generate steam by boiling water using electricity or natural gas. Electricity subplant 425 may be configured to generate electricity using mechanical generators (e.g., a steam turbine, a gas-powered generator, etc.) or other types of electricity-generating equipment (e.g., photovoltaic equipment, hydroelectric equipment, etc.).

The input resources used by subplants 420 may be provided by sources 410, retrieved from storage 430, and/or generated by other subplants 420. For example, steam subplant 424 may produce steam as an output resource. Electricity subplant 425 may include a steam turbine that uses the steam generated by steam subplant 424 as an input resource to generate electricity. The output resources produced by subplants 420 may be stored in storage 430, provided to sinks 440, and/or used by other subplants 420. For example, the electricity generated by electricity subplant 425 may be stored in electrical energy storage 433, used by chiller subplant 422 to generate cold thermal energy, used to satisfy the electric load 445 of a building, or sold to resource purchasers 441.

Storage 430 can be configured to store energy or other types of resources for later use. Each type of storage within storage 430 may be configured to store a different type of resource. For example, storage 430 is shown to include hot thermal energy storage 431 (e.g., one or more hot water storage tanks), cold thermal energy storage 432 (e.g., one or more cold thermal energy storage tanks), electrical energy storage 433 (e.g., one or more batteries), and resource type P storage 434, where P is the total number of storage 430. In some embodiments, storage 430 include some or all of the storage of central plant 200, as described with reference to FIG. 2 . In some embodiments, storage 430 includes the heat capacity of the building served by the central plant. The resources stored in storage 430 may be purchased directly from sources or generated by subplants 420.

In some embodiments, storage 430 is used by asset allocation system 400 to take advantage of price-based demand response (PBDR) programs. PBDR programs encourage consumers to reduce consumption when generation, transmission, and distribution costs are high. PBDR programs are typically implemented (e.g., by sources 410) in the form of energy prices that vary as a function of time. For example, some utilities may increase the price per unit of electricity during peak usage hours to encourage customers to reduce electricity consumption during peak times. Some utilities also charge consumers a separate demand charge based on the maximum rate of electricity consumption at any time during a predetermined demand charge period.

Advantageously, storing energy and other types of resources in storage 430 allows for the resources to be purchased at times when the resources are relatively less expensive (e.g., during non-peak electricity hours) and stored for use at times when the resources are relatively more expensive (e.g., during peak electricity hours). Storing resources in storage 430 also allows the resource demand of the building or campus to be shifted in time. For example, resources can be purchased from sources 410 at times when the demand for heating or cooling is low and immediately converted into hot or cold thermal energy by subplants 420. The thermal energy can be stored in storage 430 and retrieved at times when the demand for heating or cooling is high. This allows asset allocation system 400 to smooth the resource demand of the building or campus and reduces the maximum required capacity of subplants 420. Smoothing the demand also asset allocation system 400 to reduce the peak electricity consumption, which results in a lower demand charge.

In some embodiments, storage 430 is used by asset allocation system 400 to take advantage of incentive-based demand response (IBDR) programs. IBDR programs provide incentives to customers who have the capability to store energy, generate energy, or curtail energy usage upon request. Incentives are typically provided in the form of monetary revenue paid by sources 410 or by an independent service operator (ISO). IBDR programs supplement traditional utility-owned generation, transmission, and distribution assets with additional options for modifying demand load curves. For example, stored energy can be sold to resource purchasers 441 or an energy grid 442 to supplement the energy generated by sources 410. In some instances, incentives for participating in an IBDR program vary based on how quickly a system can respond to a request to change power output/consumption. Faster responses may be compensated at a higher level. Advantageously, electrical energy storage 433 allows system 400 to quickly respond to a request for electric power by rapidly discharging stored electrical energy to energy grid 442.

Sinks 440 may include the requested loads of a building or campus as well as other types of resource consumers. For example, sinks 440 are shown to include resource purchasers 441, an energy grid 442, a hot water load 443, a cold water load 444, an electric load 445, and sink Q, where Q is the total number of sinks 440. A building may consume various resources including, for example, hot thermal energy (e.g., hot water), cold thermal energy (e.g., cold water), and/or electrical energy. In some embodiments, the resources are consumed by equipment or subsystems within the building (e.g., HVAC equipment, lighting, computers and other electronics, etc.). The consumption of each sink 440 over the optimization period can be supplied as an input to asset allocation system 400 or predicted by asset allocation system 400. Sinks 440 can receive resources directly from sources 410, from subplants 420, and/or from storage 430.

Still referring to FIG. 4 , asset allocation system 400 is shown to include an asset allocator 402. Asset allocator 402 can be implemented as part of a controller, computing system, cloud computing resource, etc., for example as shown in FIG. 5 and described with reference thereto. Asset allocator 402 may be configured to control the distribution, production, storage, and usage of resources in asset allocation system 400. In some embodiments, asset allocator 402 performs an optimization process determine an optimal set of control decisions for each time step within an optimization period. The control decisions may include, for example, an optimal amount of each resource to purchase from sources 410, an optimal amount of each resource to produce or convert using subplants 420, an optimal amount of each resource to store or remove from storage 430, an optimal amount of each resource to sell to resources purchasers 441 or energy grid 440, and/or an optimal amount of each resource to provide to other sinks 440. In some embodiments, the control decisions include an optimal amount of each input resource and output resource for each of subplants 420.

In some embodiments, asset allocator 402 is configured to optimally dispatch all campus energy assets in order to meet the requested heating, cooling, and electrical loads of the campus for each time step within an optimization horizon or optimization period of duration h. Instead of focusing on only the typical HVAC energy loads, the concept is extended to the concept of resource. Throughout this disclosure, the term “resource” is used to describe any type of commodity purchased from sources 410, used or produced by subplants 420, stored or discharged by storage 430, or consumed by sinks 440. For example, water may be considered a resource that is consumed by chillers, heaters, or cooling towers during operation. This general concept of a resource can be extended to chemical processing plants where one of the resources is the product that is being produced by the chemical processing plat.

Asset allocator 402 can be configured to operate the equipment of asset allocation system 400 to ensure that a resource balance is maintained at each time step of the optimization period. This resource balance is shown in the following equation:

Σx _(time)=0∀resources,∀time∈horizon

where the sum is taken over all producers and consumers of a given resource (i.e., all of sources 410, subplants 420, storage 430, and sinks 440) and time is the time index. Each time element represents a period of time during which the resource productions, requests, purchases, etc. are assumed constant. Asset allocator 402 may ensure that this equation is satisfied for all resources regardless of whether that resource is required by the building or campus. For example, some of the resources produced by subplants 420 may be intermediate resources that function only as inputs to other subplants 420.

In some embodiments, the resources balanced by asset allocator 402 include multiple resources of the same type (e.g., multiple chilled water resources, multiple electricity resources, etc.). Defining multiple resources of the same type may allow asset allocator 402 to satisfy the resource balance given the physical constraints and connections of the central plant equipment. For example, suppose a central plant has multiple chillers and multiple cold water storage tanks, with each chiller physically connected to a different cold water storage tank (i.e., chiller A is connected to cold water storage tank A, chiller B is connected to cold water storage tank B, etc.). Given that only one chiller can supply cold water to each cold water storage tank, a different cold water resource can be defined for the output of each chiller. This allows asset allocator 402 to ensure that the resource balance is satisfied for each cold water resource without attempting to allocate resources in a way that is physically impossible (e.g., storing the output of chiller A in cold water storage tank B, etc.).

Asset allocator 402 may be configured to minimize the economic cost (or maximize the economic value) of operating asset allocation system 400 over the duration of the optimization period. The economic cost may be defined by a cost function J(x) that expresses economic cost as a function of the control decisions made by asset allocator 402. The cost function J(x) may account for the cost of resources purchased from sources 410, as well as the revenue generated by selling resources to resource purchasers 441 or energy grid 442 or participating in incentive programs. The cost optimization performed by asset allocator 402 can be expressed as:

$\underset{x}{\arg\min}{J(x)}$

where J(x) is defined as follows:

${J(x)} = {{\sum\limits_{sources}{\sum\limits_{horizon}{{cost}\left( {{purchase}_{{resources},{time}},{time}} \right)}}} - {\sum\limits_{incentives}{\sum\limits_{horizon}{{revenue}({ReservationAmount})}}}}$

The first term in the cost function J(x) represents the total cost of all resources purchased over the optimization horizon. Resources can include, for example, water, electricity, natural gas, or other types of resources purchased from a utility or other source 410. The second term in the cost function J(x) represents the total revenue generated by participating in incentive programs (e.g., IBDR programs) over the optimization horizon. The revenue may be based on the amount of power reserved for participating in the incentive programs. Accordingly, the total cost function represents the total cost of resources purchased minus any revenue generated from participating in incentive programs.

Each of subplants 420 and storage 430 may include equipment that can be controlled by asset allocator 402 to optimize the performance of asset allocation system 400. Subplant equipment may include, for example, heating devices, chillers, heat recovery heat exchangers, cooling towers, energy storage devices, pumps, valves, and/or other devices of subplants 420 and storage 430. Individual devices of subplants 420 can be turned on or off to adjust the resource production of each subplant 420. In some embodiments, individual devices of subplants 420 can be operated at variable capacities (e.g., operating a chiller at 10% capacity or 60% capacity) according to an operating setpoint received from asset allocator 402. Asset allocator 402 can control the equipment of subplants 420 and storage 430 to adjust the amount of each resource purchased, consumed, and/or produced by system 400.

In some embodiments, asset allocator 402 minimizes the cost function while participating in PBDR programs, IBDR programs, or simultaneously in both PBDR and IBDR programs. For the IBDR programs, asset allocator 402 may use statistical estimates of past clearing prices, mileage ratios, and event probabilities to determine the revenue generation potential of selling stored energy to resource purchasers 441 or energy grid 442. For the PBDR programs, asset allocator 402 may use predictions of ambient conditions, facility thermal loads, and thermodynamic models of installed equipment to estimate the resource consumption of subplants 420. Asset allocator 402 may use predictions of the resource consumption to monetize the costs of running the equipment.

Asset allocator 402 may automatically determine (e.g., without human intervention) a combination of PBDR and/or IBDR programs in which to participate over the optimization horizon in order to maximize economic value. For example, asset allocator 402 may consider the revenue generation potential of IBDR programs, the cost reduction potential of PBDR programs, and the equipment maintenance/replacement costs that would result from participating in various combinations of the IBDR programs and PBDR programs. Asset allocator 402 may weigh the benefits of participation against the costs of participation to determine an optimal combination of programs in which to participate. Advantageously, this allows asset allocator 402 to determine an optimal set of control decisions that maximize the overall value of operating asset allocation system 400.

In some embodiments, asset allocator 402 optimizes the cost function J(x) subject to the following constraint, which guarantees the balance between resources purchased, produced, discharged, consumed, and requested over the optimization horizon:

${{{\sum\limits_{sources}{purchase}_{{resource},{time}}} + {\sum\limits_{subplants}{{produces}\left( {x_{{internal},{time}},x_{{external},{time}},v_{{uncontrolled},{time}}} \right)}} - {\sum\limits_{subplants}{{consumes}\left( {x_{{internal},{time}},x_{{external},{time}},v_{{uncontrolled},{time}}} \right)}} + {\sum\limits_{storages}{{discharges}_{resource}\left( {x_{{internal},{time}},x_{{external},{time}}} \right)}} - {\sum\limits_{sinks}{requests}_{resource}}} = {0{\forall{resources}}}},{\forall{{time} \in {horizon}}}$

where x_(internal,time) includes internal decision variables (e.g., load allocated to each component of asset allocation system 400), x_(external,time) includes external decision variables (e.g., condenser water return temperature or other shared variables across subplants 420), and v_(uncontrolled,time) includes uncontrolled variables (e.g., weather conditions).

The first term in the previous equation represents the total amount of each resource (e.g., electricity, water, natural gas, etc.) purchased from each source 410 over the optimization horizon. The second and third terms represent the total production and consumption of each resource by subplants 420 over the optimization horizon. The fourth term represents the total amount of each resource discharged from storage 430 over the optimization horizon. Positive values indicate that the resource is discharged from storage 430, whereas negative values indicate that the resource is charged or stored. The fifth term represents the total amount of each resource requested by sinks 440 over the optimization horizon. Accordingly, this constraint ensures that the total amount of each resource purchased, produced, or discharged from storage 430 is equal to the amount of each resource consumed, stored, or provided to sinks 440.

In some embodiments, additional constraints exist on the regions in which subplants 420 can operate. Examples of such additional constraints include the acceptable space (i.e., the feasible region) for the decision variables given the uncontrolled conditions, the maximum amount of a resource that can be purchased from a given source 410, and any number of plant-specific constraints that result from the mechanical design of the plant. These additional constraints can be generated and imposed by operational domain module 904 (described in greater detail with reference to FIGS. 9 and 12 ).

Asset allocator 402 may include a variety of features that enable the application of asset allocator 402 to nearly any central plant, central energy facility, combined heating and cooling facility, or combined heat and power facility. These features include broadly applicable definitions for subplants 420, sinks 440, storage 430, and sources 410; multiples of the same type of subplant 420 or sink 440; subplant resource connections that describe which subplants 420 can send resources to which sinks 440 and at what efficiency; subplant minimum turndown into the asset allocation optimization; treating electrical energy as any other resource that must be balanced; constraints that can be commissioned during runtime; different levels of accuracy at different points in the horizon; setpoints (or other decisions) that are shared between multiple subplants included in the decision vector; disjoint subplant operation regions; incentive based electrical energy programs; and high level airside models. Incorporation of these features may allow asset allocator 402 to support a majority of the central energy facilities that will be seen in the future. Additionally, it will be possible to rapidly adapt to the inclusion of new subplant types. Some of these features are described in greater detail below.

Broadly applicable definitions for subplants 420, sinks 440, storage 430, and sources 410 allow each of these components to be described by the mapping from decision variables to resources consume and resources produced. Resources and other components of system 400 do not need to be “typed,” but rather can be defined generally. The mapping from decision variables to resource consumption and production can change based on extrinsic conditions. Asset allocator 420 can solve the optimization problem by simply balancing resource use and can be configured to solve in terms of consumed resource 1, consumed resource 2, produced resource 1, etc., rather than electricity consumed, water consumed, and chilled water produced. Such an interface at the high level allows for the mappings to be injected into asset allocation system 400 rather than needing them hard coded. Of course, “typed” resources and other components of system 400 can still exist in order to generate the mapping at run time, based on equipment out of service.

Incorporating multiple subplants 420 or sinks 440 of the same type allows for modeling the interconnections between subplants 420, sources 410, storage 430, and sinks 440. This type of modeling describes which subplants 420 can use resource from which sources 410 and which subplants 420 can send resources to which sinks 440. This can be visualized as a resource connection matrix (i.e., a directed graph) between the subplants 420, sources 410, sinks 440, and storage 430. Extending this concept, it is possible to include costs for delivering the resource along a connection and also, efficiencies of the transmission (e.g., amount of energy that makes it to the other side of the connection).

In some instances, constraints arise due to mechanical problems after an energy facility has been built. Accordingly, these constraints are site specific and are often not incorporated into the main code for any of subplants 420 or the high level problem itself. Commissioned constraints allow for such constraints to be added without software updates during the commissioning phase of the project. Furthermore, if these additional constraints are known prior to the plant build, they can be added to the design tool run. This would allow the user to determine the cost of making certain design decisions.

Incentive programs often require the reservation of one or more assets for a period of time. In traditional systems, these assets are typically turned over to alternative control, different than the typical resource price based optimization. Advantageously, asset allocator 402 can be configured to add revenue to the cost function per amount of resource reserved. Asset allocator 402 can then make the reserved portion of the resource unavailable for typical price based cost optimization. For example, asset allocator 402 can reserve a portion of a battery asset for frequency response. In this case, the battery can be used to move the load or shave the peak demand, but can also be reserved to participate in the frequency response program.

Central Plant Controller

Referring now to FIG. 5 , a block diagram of a central plant controller 500 in which asset allocator 402 can be implemented is shown, according to an exemplary embodiment. In various embodiments, central plant controller 500 can be configured to monitor and control central plant 200, asset allocation system 400, and various components thereof (e.g., sources 410, subplants 420, storage 430, sinks 440, etc.). Central plant controller 500 is shown providing control decisions to a building management system (BMS) 506. The control decisions provided to BMS 506 may include resource purchase amounts for sources 410, setpoints for subplants 420, and/or charge/discharge rates for storage 430. In other embodiments, the central plant controller is configured in a planning tool implementation in which an operation of the central plant is planned over an optimization period (e.g., 1 year) for use in planning, operational decision-making, budgeting, planning for purchase of new assets, etc.

In some embodiments, BMS 506 is the same or similar to the BMS described with reference to FIG. 1 . BMS 506 may be configured to monitor conditions within a controlled building or building zone. For example, BMS 506 may receive input from various sensors (e.g., temperature sensors, humidity sensors, airflow sensors, voltage sensors, etc.) distributed throughout the building and may report building conditions to central plant controller 500. Building conditions may include, for example, a temperature of the building or a zone of the building, a power consumption (e.g., electric load) of the building, a state of one or more actuators configured to affect a controlled state within the building, or other types of information relating to the controlled building. BMS 506 may operate subplants 420 and storage 430 to affect the monitored conditions within the building and to serve the thermal energy loads of the building.

BMS 506 may receive control signals from central plant controller 500 specifying on/off states, charge/discharge rates, and/or setpoints for the subplant equipment. BMS 506 may control the equipment (e.g., via actuators, power relays, etc.) in accordance with the control signals provided by central plant controller 500. For example, BMS 506 may operate the equipment using closed loop control to achieve the setpoints specified by central plant controller 500. In various embodiments, BMS 506 may be combined with central plant controller 500 or may be part of a separate building management system. According to an exemplary embodiment, BMS 506 is a METASYS® brand building management system, as sold by Johnson Controls, Inc.

Central plant controller 500 may monitor the status of the controlled building using information received from BMS 506. Central plant controller 500 may be configured to predict the thermal energy loads (e.g., heating loads, cooling loads, etc.) of the building for plurality of time steps in an optimization period (e.g., using weather forecasts from a weather service 504). Central plant controller 500 may also predict the revenue generation potential of incentive based demand response (IBDR) programs using an incentive event history (e.g., past clearing prices, mileage ratios, event probabilities, etc.) from incentive programs 502. Central plant controller 500 may generate control decisions that optimize the economic value of operating central plant 200 over the duration of the optimization period subject to constraints on the optimization process (e.g., energy balance constraints, load satisfaction constraints, etc.). The optimization process performed by central plant controller 500 is described in greater detail below.

In some embodiments, central plant controller 500 is integrated within a single computer (e.g., one server, one housing, etc.). In various other exemplary embodiments, central plant controller 500 can be distributed across multiple servers or computers (e.g., that can exist in distributed locations). In another exemplary embodiment, central plant controller 500 may integrated with a smart building manager that manages multiple building systems and/or combined with BMS 506.

Central plant controller 500 is shown to include a communications interface 536 and a processing circuit 507. Communications interface 536 may include wired or wireless interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with various systems, devices, or networks. For example, communications interface 536 may include an Ethernet card and port for sending and receiving data via an Ethernet-based communications network and/or a WiFi transceiver for communicating via a wireless communications network. Communications interface 536 may be configured to communicate via local area networks or wide area networks (e.g., the Internet, a building WAN, etc.) and may use a variety of communications protocols (e.g., BACnet, IP, LON, etc.).

Communications interface 536 may be a network interface configured to facilitate electronic data communications between central plant controller 500 and various external systems or devices (e.g., BMS 506, subplants 420, storage 430, sources 410, etc.). For example, central plant controller 500 may receive information from BMS 506 indicating one or more measured states of the controlled building (e.g., temperature, humidity, electric loads, etc.) and one or more states of subplants 420 and/or storage 430 (e.g., equipment status, power consumption, equipment availability, etc.). Communications interface 536 may receive inputs from BMS 506, subplants 420, and/or storage 430 and may provide operating parameters (e.g., on/off decisions, setpoints, etc.) to subplants 420 and storage 430 via BMS 506. The operating parameters may cause subplants 420 and storage 430 to activate, deactivate, or adjust a setpoint for various devices thereof.

Still referring to FIG. 5 , processing circuit 507 is shown to include a processor 508 and memory 510. Processor 508 may be a general purpose or specific purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable processing components. Processor 508 may be configured to execute computer code or instructions stored in memory 510 or received from other computer readable media (e.g., CDROM, network storage, a remote server, etc.).

Memory 510 may include one or more devices (e.g., memory units, memory devices, storage devices, etc.) for storing data and/or computer code for completing and/or facilitating the various processes described in the present disclosure. Memory 510 may include random access memory (RAM), read-only memory (ROM), hard drive storage, temporary storage, non-volatile memory, flash memory, optical memory, or any other suitable memory for storing software objects and/or computer instructions. Memory 510 may include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present disclosure. Memory 510 may be communicably connected to processor 508 via processing circuit 507 and may include computer code for executing (e.g., by processor 508) one or more processes described herein.

Memory 510 is shown to include a building status monitor 524. Central plant controller 500 may receive data regarding the overall building or building space to be heated or cooled by system 400 via building status monitor 524. In an exemplary embodiment, building status monitor 524 may include a graphical user interface component configured to provide graphical user interfaces to a user for selecting building requirements (e.g., overall temperature parameters, selecting schedules for the building, selecting different temperature levels for different building zones, etc.).

Central plant controller 500 may determine on/off configurations and operating setpoints to satisfy the building requirements received from building status monitor 524. In some embodiments, building status monitor 524 receives, collects, stores, and/or transmits cooling load requirements, building temperature setpoints, occupancy data, weather data, energy data, schedule data, and other building parameters. In some embodiments, building status monitor 524 stores data regarding energy costs, such as pricing information available from sources 410 (energy charge, demand charge, etc.).

Still referring to FIG. 5 , memory 510 is shown to include a load/rate predictor 522. Load/rate predictor 522 may be configured to predict the thermal energy loads (

_(k)) of the building or campus for each time step k (e.g., k=1 . . . n) of an optimization period. Load/rate predictor 522 is shown receiving weather forecasts from a weather service 504. In some embodiments, load/rate predictor 522 predicts the thermal energy loads

_(k) as a function of the weather forecasts. In some embodiments, load/rate predictor 522 uses feedback from BMS 506 to predict loads

_(k). Feedback from BMS 506 may include various types of sensory inputs (e.g., temperature, flow, humidity, enthalpy, etc.) or other data relating to the controlled building (e.g., inputs from a HVAC system, a lighting control system, a security system, a water system, etc.).

In some embodiments, load/rate predictor 522 receives a measured electric load and/or previous measured load data from BMS 506 (e.g., via building status monitor 524). Load/rate predictor 522 may predict loads

_(k) as a function of a given weather forecast ({circumflex over (ϕ)}_(w)), a day type (day), the time of day (t), and previous measured load data (Y_(k−1)). Such a relationship is expressed in the following equation:

_(k) =f({circumflex over (ϕ)}_(w),day,t|Y _(k−1))

In some embodiments, load/rate predictor 522 uses a deterministic plus stochastic model trained from historical load data to predict loads

_(k). Load/rate predictor 522 may use any of a variety of prediction methods to predict loads

_(k) (e.g., linear regression for the deterministic portion and an AR model for the stochastic portion). Load/rate predictor 522 may predict one or more different types of loads for the building or campus. For example, load/rate predictor 522 may predict a hot water load

_(Hot,k) and a cold water load

_(Cold,k) for each time step k within the prediction window. In some embodiments, load/rate predictor 522 makes load/rate predictions using the techniques described in U.S. patent application Ser. No. 14/717,593.

Load/rate predictor 522 is shown receiving utility rates from sources 410. Utility rates may indicate a cost or price per unit of a resource (e.g., electricity, natural gas, water, etc.) provided by sources 410 at each time step k in the prediction window. In some embodiments, the utility rates are time-variable rates. For example, the price of electricity may be higher at certain times of day or days of the week (e.g., during high demand periods) and lower at other times of day or days of the week (e.g., during low demand periods). The utility rates may define various time periods and a cost per unit of a resource during each time period. Utility rates may be actual rates received from sources 410 or predicted utility rates estimated by load/rate predictor 522.

In some embodiments, the utility rates include demand charges for one or more resources provided by sources 410. A demand charge may define a separate cost imposed by sources 410 based on the maximum usage of a particular resource (e.g., maximum energy consumption) during a demand charge period. The utility rates may define various demand charge periods and one or more demand charges associated with each demand charge period. In some instances, demand charge periods may overlap partially or completely with each other and/or with the prediction window. Advantageously, demand response optimizer 530 may be configured to account for demand charges in the high level optimization process performed by asset allocator 402. Sources 410 may be defined by time-variable (e.g., hourly) prices, a maximum service level (e.g., a maximum rate of consumption allowed by the physical infrastructure or by contract) and, in the case of electricity, a demand charge or a charge for the peak rate of consumption within a certain period. Load/rate predictor 522 may store the predicted loads

_(k) and the utility rates in memory 510 and/or provide the predicted loads

_(k) and the utility rates to demand response optimizer 530.

Still referring to FIG. 5 , memory 510 is shown to include an incentive estimator 520. Incentive estimator 520 may be configured to estimate the revenue generation potential of participating in various incentive-based demand response (IBDR) programs. In some embodiments, incentive estimator 520 receives an incentive event history from incentive programs 502. The incentive event history may include a history of past IBDR events from incentive programs 502. An IBDR event may include an invitation from incentive programs 502 to participate in an IBDR program in exchange for a monetary incentive. The incentive event history may indicate the times at which the past IBDR events occurred and attributes describing the IBDR events (e.g., clearing prices, mileage ratios, participation requirements, etc.). Incentive estimator 520 may use the incentive event history to estimate IBDR event probabilities during the optimization period.

Incentive estimator 520 is shown providing incentive predictions to demand response optimizer 530. The incentive predictions may include the estimated IBDR probabilities, estimated participation requirements, an estimated amount of revenue from participating in the estimated IBDR events, and/or any other attributes of the predicted IBDR events. Demand response optimizer 530 may use the incentive predictions along with the predicted loads

_(k) and utility rates from load/rate predictor 522 to determine an optimal set of control decisions for each time step within the optimization period.

Still referring to FIG. 5 , memory 510 is shown to include a demand response optimizer 530. Demand response optimizer 530 may perform a cascaded optimization process to optimize the performance of asset allocation system 400. For example, demand response optimizer 530 is shown to include asset allocator 402 and a low level optimizer 534. Asset allocator 402 may control an outer (e.g., subplant level) loop of the cascaded optimization. Asset allocator 402 may determine an optimal set of control decisions for each time step in the prediction window in order to optimize (e.g., maximize) the value of operating asset allocation system 400. Control decisions made by asset allocator 402 may include, for example, load setpoints for each of subplants 420, charge/discharge rates for each of storage 430, resource purchase amounts for each type of resource purchased from sources 410, and/or an amount of each resource sold to energy purchasers 504. In other words, the control decisions may define resource allocation at each time step. The control decisions made by asset allocator 402 are based on the statistical estimates of incentive event probabilities and revenue generation potential for various IBDR events as well as the load and rate predictions.

Low level optimizer 534 may control an inner (e.g., equipment level) loop of the cascaded optimization. Low level optimizer 534 may determine how to best run each subplant at the load setpoint determined by asset allocator 402. For example, low level optimizer 534 may determine on/off states and/or operating setpoints for various devices of the subplant equipment in order to optimize (e.g., minimize) the energy consumption of each subplant while meeting the resource allocation setpoint for the subplant. In some embodiments, low level optimizer 534 receives actual incentive events from incentive programs 502. Low level optimizer 534 may determine whether to participate in the incentive events based on the resource allocation set by asset allocator 402. For example, if insufficient resources have been allocated to a particular IBDR program by asset allocator 402 or if the allocated resources have already been used, low level optimizer 534 may determine that asset allocation system 400 will not participate in the IBDR program and may ignore the IBDR event. However, if the required resources have been allocated to the IBDR program and are available in storage 430, low level optimizer 534 may determine that system 400 will participate in the IBDR program in response to the IBDR event. The cascaded optimization process performed by demand response optimizer 530 is described in greater detail in U.S. patent application Ser. No. 15/247,885.

In some embodiments, low level optimizer 534 generates and provides subplant curves to asset allocator 402. Each subplant curve may indicate an amount of resource consumption by a particular subplant (e.g., electricity use measured in kW, water use measured in L/s, etc.) as a function of the subplant load. In some embodiments, low level optimizer 534 generates the subplant curves by running the low level optimization process for various combinations of subplant loads and weather conditions to generate multiple data points. Low level optimizer 534 may fit a curve to the data points to generate the subplant curves. In other embodiments, low level optimizer 534 provides the data points asset allocator 402 and asset allocator 402 generates the subplant curves using the data points. Asset allocator 402 may store the subplant curves in memory for use in the high level (i.e., asset allocation) optimization process.

In some embodiments, the subplant curves are generated by combining efficiency curves for individual devices of a subplant. A device efficiency curve may indicate the amount of resource consumption by the device as a function of load. The device efficiency curves may be provided by a device manufacturer or generated using experimental data. In some embodiments, the device efficiency curves are based on an initial efficiency curve provided by a device manufacturer and updated using experimental data. The device efficiency curves may be stored in equipment models 518. For some devices, the device efficiency curves may indicate that resource consumption is a U-shaped function of load. Accordingly, when multiple device efficiency curves are combined into a subplant curve for the entire subplant, the resultant subplant curve may be a wavy curve. The waves are caused by a single device loading up before it is more efficient to turn on another device to satisfy the subplant load.

In some embodiments, low level optimizer 634 generates the subplant curves by running the low level optimization process for various combinations of subplant loads and weather conditions to generate multiple data points. Low level optimizer 634 may fit a curve to the data points to generate the subplant curves. In other embodiments, low level optimizer 634 provides the data points to asset allocator 402 and asset allocator 402 generates the subplant curves using the data points. Asset allocator 402 may store the subplant curves for use in the high level optimization process.

The asset allocator 402 may be configured to convert the subplant curves into convex curves, including automatically into multiple convex curves as described below with reference to FIG. 6 . A convex curve is a curve for which a line connecting any two points on the curve is always above or along the curve (i.e., not below the curve). Convex curves may be advantageous for use in the high level optimization by the asset allocator 402 because they allow for an optimization process that is less computationally expensive relative to an optimization process that uses non-convex functions. The subplant curves may be defined by piecewise linear segments that combine to form a piecewise-defined convex curve. The subplant curves may thus be made of multiple linearized convex portions which reduce computational complexity relative to other possible implementations.

The asset allocator 402 can updated the high level optimization problem to incorporate the subplant curves into the optimization. For example, the decision variables can include one or more decision vectors representing the resource consumption of each subplant and inequality constraints can be modified using the subplant curves to ensure that the proper amount of each resource is consumed to serve the predicted thermal energy loads. In some embodiments, the asset allocator 402 formulates inequality constraints that force the resource usage for each resource in the epigraph of the corresponding linearized subplant curve. For example, chiller subplant 422 may have a linearized subplant curve that indicates the electricity use of chiller subplant 422 (i.e., input resource in₁) as a function of the cold water production of chiller subplant 422 (i.e., output resource outs). The linearized subplant curve may include a first line segment connecting point [u₁, Q₁] to point [u₂, Q₂], a second line segment connecting point [u₂, Q₂] to point [u₃, Q₃], and a third line segment connecting point [u₃, Q₃] to point [u₄, Q₄].

The asset allocator 402 may formulate an inequality constraint for each piecewise segment of the subplant curve that constrains the value of the decision variable representing chiller electricity use to be greater than or equal to the amount of electricity use defined by the line segment for the corresponding value of the cold water production. Similar inequality constraints can be formulated for other subplant curves. For example, the asset allocator 402 may generate a set of inequality constraints for the water consumption of chiller subplant 422 using the points defining the linearized subplant curve for the water consumption of chiller subplant 422 as a function of cold water production. In some embodiments, the water consumption of chiller subplant 422 is equal to the cold water production and the linearized subplant curve for water consumption includes a single line segment connecting point [u₅, Q₅] to point [u₆, Q₆]. The asset allocator 402 may repeat this process for each subplant curve for chiller subplant 522 and for the other subplants of the central plant to define a set of inequality constraints for each subplant curve.

Such inequality constraints ensure that asset keeps the resource consumption above all of the line segments of the corresponding subplant curve. In most situations, there is no reason for asset allocator 402 to choose a resource consumption value that lies above the corresponding subplant curve due to the economic cost associated with resource consumption. Asset allocator 402 can therefore be expected to select resource consumption values that lie on the corresponding subplant curve rather than above it.

The exception to this general rule is heat recovery chiller subplant 423. The equality constraints for heat recovery chiller subplant 423 provide that heat recovery chiller subplant 423 produces hot water at a rate equal to the subplant's cold water production plus the subplant's electricity use. The inequality constraints for heat recovery chiller subplant 423 allow asset allocator 402 to overuse electricity to make more hot water without increasing the amount of cold water production. This behavior is extremely inefficient and only becomes a realistic possibility when the demand for hot water is high and cannot be met using more efficient techniques. However, this is not how heat recovery chiller subplant 423 actually operates.

To prevent asset allocator 402 from overusing electricity, asset allocator 402 may check whether the calculated amount of electricity use (determined by the optimization algorithm) for heat recovery chiller subplant 423 is above the corresponding subplant curve. In some embodiments, the check is performed after each iteration of the optimization algorithm. If the calculated amount of electricity use for heat recovery chiller subplant 423 is above the subplant curve, a determining is made that the asset allocator 402 is overusing electricity. In response to a determination that asset allocator 402 is overusing electricity, the production of heat recovery chiller subplant 523 can be constrained at its current value and the electricity use of subplant 523 can be constrained to the corresponding value on the subplant curve. Asset allocator 402 may then rerun the optimization with the new equality constraints. These and other features of relating to subplant curves are described in greater detail in U.S. patent application Ser. No. 14/634,609 filed Feb. 27, 2015, the entire disclosure of which is incorporated by reference herein.

Still referring to FIG. 5 , memory 510 is shown to include a subplant control module 528. Subplant control module 528 may store historical data regarding past operating statuses, past operating setpoints, and instructions for calculating and/or implementing control parameters for subplants 420 and storage 430. Subplant control module 528 may also receive, store, and/or transmit data regarding the conditions of individual devices of the subplant equipment, such as operating efficiency, equipment degradation, a date since last service, a lifespan parameter, a condition grade, or other device-specific data. Subplant control module 528 may receive data from subplants 420, storage 430, and/or BMS 506 via communications interface 536. Subplant control module 528 may also receive and store on/off statuses and operating setpoints from low level optimizer 534.

Data and processing results from demand response optimizer 530, subplant control module 528, or other modules of central plant controller 500 may be accessed by (or pushed to) monitoring and reporting applications 526. Monitoring and reporting applications 526 may be configured to generate real time “system health” dashboards that can be viewed and navigated by a user (e.g., a system engineer). For example, monitoring and reporting applications 526 may include a web-based monitoring application with several graphical user interface (GUI) elements (e.g., widgets, dashboard controls, windows, etc.) for displaying key performance indicators (KPI) or other information to users of a GUI. In addition, the GUI elements may summarize relative energy use and intensity across energy storage systems in different buildings (real or modeled), different campuses, or the like. Other GUI elements or reports may be generated and shown based on available data that allow users to assess performance across one or more energy storage systems from one screen. The user interface or report (or underlying data engine) may be configured to aggregate and categorize operating conditions by building, building type, equipment type, and the like. The GUI elements may include charts or histograms that allow the user to visually analyze the operating parameters and power consumption for the devices of the energy storage system.

Still referring to FIG. 5 , central plant controller 500 may include one or more GUI servers, web services 512, or GUI engines 514 to support monitoring and reporting applications 526. In various embodiments, applications 526, web services 512, and GUI engine 514 may be provided as separate components outside of central plant controller 500 (e.g., as part of a smart building manager). Central plant controller 500 may be configured to maintain detailed historical databases (e.g., relational databases, XML databases, etc.) of relevant data and includes computer code modules that continuously, frequently, or infrequently query, aggregate, transform, search, or otherwise process the data maintained in the detailed databases. Central plant controller 500 may be configured to provide the results of any such processing to other databases, tables, XML files, or other data structures for further querying, calculation, or access by, for example, external monitoring and reporting applications.

Central plant controller 500 is shown to include configuration tools 516. Configuration tools 516 can allow a user to define (e.g., via graphical user interfaces, via prompt-driven “wizards,” etc.) how central plant controller 500 should react to changing conditions in the energy storage subsystems. In an exemplary embodiment, configuration tools 516 allow a user to build and store condition-response scenarios that can cross multiple energy storage system devices, multiple building systems, and multiple enterprise control applications (e.g., work order management system applications, entity resource planning applications, etc.). For example, configuration tools 516 can provide the user with the ability to combine data (e.g., from subsystems, from event histories) using a variety of conditional logic. In varying exemplary embodiments, the conditional logic can range from simple logical operators between conditions (e.g., AND, OR, XOR, etc.) to pseudo-code constructs or complex programming language functions (allowing for more complex interactions, conditional statements, loops, etc.). Configuration tools 516 can present user interfaces for building such conditional logic. The user interfaces may allow users to define policies and responses graphically. In some embodiments, the user interfaces may allow a user to select a pre-stored or pre-constructed policy and adapt it or enable it for use with their system.

Various other implementations of the cost functions, optimization processes, controllers, etc. described above are also possible. For example, the systems and methods described herein may be implemented with any combination of the various features described in U.S. patent application Ser. No. 15/405,236, filed Jan. 12, 2017; U.S. patent application Ser. No. 15/405,234, filed Jan. 12, 2017; U.S. patent application Ser. No. 15/429,962, filed Feb. 7, 2017; U.S. patent application Ser. No. 15/473,496, filed Mar. 29, 2017; U.S. patent application Ser. No. 15/616,616, filed Jun. 7, 2017; U.S. patent application Ser. No. 16/115,290, filed Aug. 28, 2018; U.S. patent application Ser. No. 16/260,030, filed Jan. 27, 2019; and U.S. patent application Ser. No. 17/668,791, filed Feb. 10, 2022; U.S. Pat. No. 11,221,156, granted Jan. 11, 2022; and U.S. Pat. No. 9,612,601, granted Apr. 4, 2017. These applications are incorporated by reference herein in their entireties.

Automatic Creation of Subplant Curves

Referring now to FIG. 6 , a flowchart of a process 600 for automatic creation of a subplant curve is shown, according to some embodiments. Process 600 can be executed by the central plant controller 500, for example by low level optimizer 534, the asset allocator 402, and/or a combination thereof in various embodiments. Process 600 can be separately executed for each of multiple subplants of a central plant. The following description of process 600 also refers to FIG. 7 , which shows a set 700 of graphs for a two-dimensional example scenario according to some embodiments, and FIG. 8 , which shows a set 800 of graphs for a three-dimensional example scenario according to some embodiments.

At step 602, data points are obtained representing subplant performance, including pairs of values of an independent variable (e.g., resource production, heating or cooling energy produced) and a dependent variable (e.g., resource consumption, electricity usage) for a subplant. Subplant performance data can also be higher-dimensional, for example including additional independent variables (e.g., environmental conditions such as wet bulb temperature) and/or dependent variables (e.g., emissions, pollution, etc.).

Examples of subplant performance data that can be obtained in various embodiments are shown in FIGS. 7 and 8 . A first graph 702 of the set 700 of FIG. 7 shows a plot of data points, in particular values of electricity consumption for a set of values of chilled water production. A first graph 802 of the set 800 of FIG. 8 shows a plot of data points, in particular values of electricity consumption for sets of values of chilled water production and wet bulb temperature (e.g., outside air temperature). In the example of FIG. 8 , the subplant performance data includes values of electricity consumption at three wet bulb temperatures (shown as fifty degrees, sixty degrees, and seventy degrees) for each of set of equally-space values of chilled water production.

At step 604, for all data points, values of a convexity metric a dependent variable with respect to an independent variable are calculated, shown in the examples herein as a second derivatives of the dependent variable with respect to the independent variable. In the example of FIG. 7 , step 604 includes calculating second derivatives of electricity consumption with respect to chilled water, i.e., a value characterizing a rate of change of the rate at which electricity consumption increases as chilled water increases. In the example of FIG. 8 , step 604 also includes calculating second derivatives of electricity consumption with respect to chilled water, with values of wet bulb temperature held constant for such calculations. In such examples, the second derivatives represent a rate of change of the rate at which electricity consumption increases as chilled water increases at constant wet bulb temperature.

In some examples, calculating the second derivatives can be performed using a finite difference method. In the examples, values of the independent variable (denoted as P) are equally separated with a sample rate equal to Δ=P_(i+1)−P_(i). The second derivative of the dependent variable (denoted as C) can then be approximated as (C_(i+1)−2C_(i)+C_(i−1))/Δ and calculated from the discrete data points obtained in step 602. The second derivative can be calculated for all data points in step 604, in some examples, but may be calculated for only a subset in other examples.

At step 606, data points with convexity metrics which exceed a threshold are flagged, for example by flagging data points with negative second derivatives (i.e., beyond a threshold of zero in the negative direction). Data points with negative data points are points of non-convexity, as a convex region will have non-negative second derivatives. In the example of FIG. 7 , graph 704 shows that a point 705 sits above a linearized convex curve connecting all other points. A calculation using such a curve would thus provide an incorrect value at a value of the chilled water production for the first point 705 (i.e., estimating lower than actual electricity consumption. It can also be seen that a rate of upward change of electricity consumption with respect to chilled water slows at the point 705. A similar point 805 is shows in a second graph 804 of FIG. 8 . Flagging data points with negative second derivatives allows step 606 to identify all such points of non-convexity.

At step 608, the flagged data points are ranked form most negative second derivative to least negative second derivative (i.e., greatest to least in second derivative absolute value) (e.g., greatest to least amount by which the convexity metrics exceed the threshold). Such a ranking provides a manner of ranking the associated errors that are caused by multiple non-convexities. The flagged data points are thus ranked from most sever non-convexity to least-sever non-convexity.

At step 610, an operating region is split at the flagged data point with the most negative second derivative. In the example of FIG. 7 , an operating region is split at point 705, because point 705 is the only flagged data point in that example and thus has the most negative (and only negative) second derivative. As shown in a third graph 706 of FIG. 7 , an operating region is split into a first region 707 on a first side of the point 705 and a second region 708 on a second, opposite side of the point 705 so that the point 705 separates the first region 707 and the second region 708. In the example of FIG. 8 , an operating region is split into a first region 807 and a second region 808 across a line defined by the point 805 having a negative second derivative. The line has a constant value of chilled water production equal to the value for the point 805.

Step 610 thus provides a first, initial split of the operating region, while in various embodiments and scenarios there are one or more additional points with negative second derivatives. Accordingly, following the split in step 610, process 600 proceeds to step 612 where a decision is made as to whether a criterion is satisfied. In some embodiments, a single criterion is assessed and considered in step 612. In other embodiments, satisfaction of any one of multiple criteria being assessed in step 612 results in an affirmative answer (“yes”) from step 612. One example of a criterion that may be used in step 612 is a user-selected maximum number of splits (or maximum number of separate convex regions), such that step 612 includes counting the number of current splits and comparing that number rot the maximum number to determine if the number has been reached (such that the criterion is satisfied) or is less than the maximum number (such that the criterion is not yet satisfied). As another example, the criterion can include assessing an accuracy of a model resulting from the current number of splits and determine whether the resulting accuracy is sufficient (e.g., satisfies a threshold accuracy or threshold error). The threshold can be user-selected. In such examples, calculations as described below with reference to FIG. 9 can be used. As another example, the criterion may be whether there are any more points with negative second derivatives remaining (i.e., that have not yet been used to split an operating region). In such an example, the scenarios of FIGS. 7 and 8 would lead to “yes” from step 612 on a first iteration of step 612.

If the criterion is not satisfied (e.g., if a maximum number of splits has not been reached, a threshold accuracy is not attained, more points with negative second derivatives are available) (“no” from step 612), the process 600 proceeds to step 614 where the operating region is split again, now at the data point with the next most negative second derivative. Step 614 includes further sub-dividing a region created in step 614 (e.g., resulting in three regions). In such an example, a third region may be created so that a second split (second data point with negative second derivative) separates a first region from the new, third region. The updated, multi-split regions are then provided back as an input to step 612. Steps 612 and 614 execute iteratively until the criterion is determined to be satisfied in step 612.

Once the criterion is satisfied (yes in step 612), the process 600 proceeds to step 616 where a subplant curve is established which includes convex curves separated by each split of the operating region. In the examples of FIGS. 7 and 8 which include one split of the operating regions, two convex curves are established on either side of the point 705 in FIG. 7 and on either side of the point 805 in FIG. 8 . The convex curves established in step 616 may be piecewise linear functions defining linear paths between data points, for example lines between adjacent data points while skipping points with negative second derivatives that do not define an endpoint of a convex curve. The number of convex curves will be one greater than the number of splits.

At step 618, equipment is controlled by performing predictive control operations based on the subplant curve created in step 616. Process 600 can also be executed additional times to determine additional subplant curves for additional subplants and/or to adjust a subplant curve in view of new operating data. For example, step 618 can include executing the various operations of the central plant controller 500 described above and using the subplant curve(s) from one or more executions of process 600. Process 600 thereby reduces or eliminates expert manual intervention in creating subplant curves for uses in performing the asset allocation and predictive control processes described herein.

Referring now to FIG. 9 , an illustration 900 illustrating a process for error or accuracy calculations relating to convex curves and subplant curves relative to operating data is shown, according to some embodiments. FIG. 9 shows the same example data from FIG. 7 , including discrete values of energy consumption for discrete values of chilled water production. As shown, a convex region 902 is defined by a convex curve 904 connecting all points except the point 705 which is an inflection point (point of non-convexity, point with negative second derivative) and a upper bound line 906 connecting end points of the convex region 904. As shown, the point 706 is above the convex curve 904, such that using the convex curve 904 to predict or estimate the electricity consumption at the corresponding chilled water production (shown as 500) would result in an underestimate of the actual energy consumption, leaving an error (inaccuracy, etc.).

In order to determine the amount of inaccuracy, which may be more difficult in higher dimensions, a process may be executed by the systems herein whereby the system runs a sweep through values of the dependent variable (electricity consumption in FIG. 9 ) for a fixed value of the independent variable (chilled water production producing 500 units in FIG. 9 ) to determine points along the line 908 illustrated in FIG. 9 (or at least points of the line 908 below the line 906 or below the point 705). The points are then assessed to determine whether they lie in the convex region (convex hull) 904, for example using barycentric coordinate. The barycentric coordinates of a point must be positive for the point to be inside the convex hull, and having any negative barycentric coordinates coefficients implies that a point lies outside the convex hull. Barycentric coordinates use a triangle in 2-D, a tetrahedron in 3-D, etc. So, in the example having a simplex with many vertices in 2-D, all possible triangles from the vertices can be calculated and then the barycentric coordinate location of a given point computed in reference to all triangles' vertices. If at least one of the triangles has all positive coefficients, then the point is inside the convex hull. On the other hand, if all of the triangles have coefficients containing at least one negative number, then the point is outside the convex hull. Such an understanding is extendable to higher dimensions and executable automatically to determine whether points are inside the convex hull 904.

Once the points inside the convex hull 904 are determine, the point in that group having the lost value of the dependent variable (e.g., lowest resource consumption) is selected and compared to the data point (e.g., point 705) such that a difference between those points is the error or inaccuracy associated with the convex curve 902. Such errors can be used to assess whether the region should be split (e.g., in step 612) and/or to otherwise compensate for such known errors.

Configuration of Exemplary Embodiments

The construction and arrangement of the systems and methods as shown in the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements can be reversed or otherwise varied and the nature or number of discrete elements or positions can be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps can be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions can be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present disclosure.

As utilized herein, the terms “approximately,” “about,” “substantially,” and similar terms are intended to have a broad meaning in harmony with the common and accepted usage by those of ordinary skill in the art to which the subject matter of this disclosure pertains. It should be understood by those of skill in the art who review this disclosure that these terms are intended to allow a description of certain features described and claimed without restricting the scope of these features to the precise numerical ranges provided. Accordingly, these terms should be interpreted as indicating that insubstantial or inconsequential modifications or alterations of the subject matter described and are considered to be within the scope of the disclosure.

The present disclosure contemplates methods, systems and program products on any machine-readable media for accomplishing various operations. The embodiments of the present disclosure can be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Embodiments within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions. 

What is claimed is:
 1. A method of operating a campus subplant, comprising: finding, in subplant performance data points defined by values of an independent variable and values of a dependent variable, a first point for which a convexity metric of the dependent variable with respect to the independent variable exceeds a threshold; creating a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point; and controlling the campus subplant based on the subplant curve.
 2. The method of claim 1, further comprising finding, in the subplant performance data points, a second point for which the convexity metric exceeds the threshold, wherein creating the subplant curve comprises: providing the first convex region between the first point and the second point; and providing a third convex region such that the second point is between the first convex region and the third convex region.
 3. The method of claim 2, wherein: the convexity metric is a second derivative; the threshold is zero; and the convexity metric exceeds the threshold when the second derivative is less than zero.
 4. The method of claim 3, wherein: the method comprises calculating the second derivatives for the subplant performance data points and ranking a subset of the subplant performance data points from most negative second derivative to least negative second derivative; the first point has the most negative second derivative; and the second point has a next most negative second derivative.
 5. The method of claim 1, further comprising: in response to the subplant curve satisfying a criterion, providing the subplant curve for use in controlling the campus subplant; and in response to the subplant curve not satisfying the criterion, splitting the first convex region or the second convex region at a second point for which the convexity metric exceeds the threshold.
 6. The method of claim 5, wherein the criterion is at least one of a maximum number of convex regions, an accuracy threshold, or that the convexity metric does not exceed the threshold for a remainder of the subplant performance data points.
 7. The method of claim 1, wherein controlling the campus subplant based on the subplant curve comprises performing an optimization subject to a constraint based on the subplant curve to determine control decisions for the campus subplant.
 8. The method of claim 1, wherein the independent variable represents production by the campus subplant and the dependent variable represents consumption by the campus subplant.
 9. Non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising: finding, in subplant performance data points defined by values of an independent variable and values of a dependent variable, a first point for which a convexity metric of the dependent variable with respect to the independent variable exceeds a threshold; creating a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point; and controlling a campus subplant based on the subplant curve.
 10. The non-transitory computer-readable media of claim 9, the operations further comprising finding, in the subplant performance data points, a second point for which the convexity metric exceeds the threshold, wherein creating the subplant curve comprises: providing the first convex region between the first point and the second point; and providing a third convex region such that the second point is between the first convex region and the third convex region.
 11. The non-transitory computer-readable media of claim 10, wherein: the operations comprise calculating the convexity metrics for the subplant performance data points and ranking a subset of the subplant performance data points by amounts by which the convexity metrics exceed the threshold; the first point has the convexity metric which exceeds the threshold by a greatest amount; and the second point has the convexity metric which exceeds the threshold by a next greatest amount.
 12. The non-transitory computer-readable media of claim 9, wherein: the convexity metric is a second derivative; the threshold is zero; and the convexity metric exceeds the threshold when the second derivative is less than zero.
 13. The non-transitory computer readable media of claim 9, the operations further comprising: in response to the subplant curve satisfying a criterion, providing the subplant curve for use in controlling the campus subplant; and in response to the subplant curve not satisfying the criterion, splitting the first convex region or the second convex region at a second point for which the convexity metric exceeds the threshold.
 14. The non-transitory computer readable media of claim 13, wherein the criterion is satisfied if a maximum number of convex regions is reached, an accuracy threshold is reached, or the convexity metric does not exceed the threshold for a remainder of the subplant performance data points.
 15. The non-transitory computer readable media of claim 9, wherein controlling the campus subplant based on the subplant curve comprises performing an optimization subject to a constraint based on the subplant curve to determine control decisions for the campus subplant.
 16. The non-transitory computer readable media of claim 9, wherein the independent variable represents production by the campus subplant and the dependent variable represents consumption by the campus subplant.
 17. A central plant, comprising: a subplant operable to consume a first resource and produce a second resource according to a set of subplant performance data points relating consumption amounts to production amounts; circuitry programmed to: find a first point in the subplant performance data points for which a convexity metric of the consumption amounts with respect to the production amounts exceeds a threshold; create a subplant curve by providing a first convex region on a first side of the first point and a second convex region on a second side of the first point; and control the subplant to consume the first resource and produce the second resource by executing control logic that uses the subplant curve.
 18. The central plant of claim 17, wherein the circuitry is further programmed to: compare the subplant curve to a criterion; in response to the subplant curve satisfying the criterion, use the subplant curve in the control logic; and in response to the subplant curve not satisfying the criterion, split the first convex region or the second convex region at an additional point for which the convexity metric exceeds the threshold before using the subplant curve in the control logic.
 19. The central plant of claim 18, wherein the criterion is a maximum number of convex regions or an accuracy threshold.
 20. The central plant of claim 17, wherein: the convexity metric is a second derivative; the threshold is zero; and the convexity metric exceeds the threshold when the second derivative is less than zero. 